The position of atoms within a molecule in three dimensional space is very important in understanding the reactivity of compounds.
The following topics are to be considered:
Conformers are not isomers. Instead, they are equivalent structures that arise as a result of the rotation of carbon atoms about a sigma bond. Usually at normal room temperatures, the different conformers are not distinguishable because the energy required to convert from one conformer to another due to rotation about a sigma bond is small enough to allow the conversion to occur very rapidly and rotation to be unhindered. It is somewhat like a camera that is incapable of recording rapid movement of an event because its shutter speed is too slow. Instruments are incapable of detecting the existence of different conformers because the speed of rotation is too fast at room temperature where there is more than enough energy to convert through the conformers as rotation occurs about the sigma bond. However, if one lowers the temperature of the environment, this slows molecular motion and eventually the rotational speed is slowed to the point where instruments are capable of recording differences between conformers. Indeed the lowering of the amount of Kinetic Energy available to cause rotation about the sigma bond will eventually be restricted enough so that rotation is stopped, and the molecule settles for the most stable conformer. This study of the energy relations between conformers is called "Conformational Analysis".
Return to the top of the page
Ethane has two basic conformers. In one, the hydrogens of the first carbon are staggered between the Hydrogens of the second carbon (See Fig 1-a below). We can show this using a perception of the molecule which takes an end view of the Ethane molecule. This is called a Newman Projection (See Fig 1-a). The second conformer is where the Hydrogens of the first carbon are lined up behind the Hydrogens of the second carbon. This is called the eclipsed conformer. (See Fig 1-b below). The staggered conformer is the most stable by 2.8 kcal/mole because the Hydrogens in the staggered conformer are fartherest away from one another and therefore do not physically hinder each other as much. This hindrance because atoms are too close to each other is called Van Der Waals Strain (Steric Strain). This steric strain is minimized in the staggered conformer. Furthermore, the sigma bonding pairs holding the Hydrogen atoms to the carbons are as far away from each other as possible. Since electrons repel each other, and this repulsion causes instability the bonding electron pairs in the staggered conformer are as far away as possible, and therefore, their repulsion is minimized thereby maximizing the stability of the molecule. This repulsion of sigma bonding pairs on adjacent carbons is called "torsional strain" In the eclipsed conformer, the amount of steric strain and the tortional strain is much increased thus making the molecule less stable.
For these reasons the staggered conformer is the preferred conformer and is the one Ethane assumes at very low temperatures. Since the 2.8 kcal/mole difference between the two conformers is so small, there is more than enough energy to overcome this energy barrier and allow the rotation to occur rapidly enough to not allow the detection of the differences between the two conformers.(See Fig 2 below)
Return to the top of the page
The free rotation of the C2 and C3 carbons of Butane give rise to several conformers that differ in their energy states. The most stable of the six conformers of Butane is the Anti conformer (See Fig 3-a below) where the two end CH3 groups (The C1 and C4 carbons of Butane) are as far away from each other as possible. This minimizes any van der waals strain that would occur between the two CH3 groups. In addition, the bonding pairs on adjacent carbons are staggered which will minimize the torsional strain that would exist between these bonding pairs. Therefore the anti conformer will have the lowest energy state of all the six conformers (See Fig 4-a)
If we rotate about the sigma bond between the second and third carbons (C2 and C3) we arrive 60 degrees of rotation to one of the eclipsed conformers where the methyl and the Hydrogen on the C2 and C3 carbons are closest to one another. (See Fig 3-b below) This increases the van der waals strain since the Hydrogen atom and the methyl groups are very close. In addition, the torsional strain would be increased, and this conformer is 3.8 kcal/mole more in energy than the anti conformer and is less stable than the anti (See Fig 4-b).
Another 60 degree rotation about the C2 and C3 sigma bond will place the methyl groups representing the C1 and C4 carbons as close to each other as possible. This eclipsed conformer (See Fig 3-d above) has maximum van der waals strain since the bulky methyl groups are rubbing up against each other and strongly repeling each other. In addition, the bonding pairs on the C2 and C3 carbons are eclipsing one another maximizing the torsional strain. This eclipsed conformer is the highest in energy being 4.5 kcal/mole more in energy than the anti conformer, and is the least stable of the six conformers. (See Fig 4-d below)
Another 60 degree rotation (the fourth such rotation since the anti conformer) will lead to another gauche conformer where the methyl groups (C1 and C4 carbons) are about as far away from each other as in the first gauche conformer (See Fig 3-e above). This gauche conformer is equivalent to the first gauche conformer in the amount of van der waals strain and torsional strain it possesses so it has the same energy state( 0.9 kcal/mole more than the anti)(See Fig 4-e below)
A fifth 60 degree rotation will give us a third eclipsed conformer(See Fig 3-f above) which in terms of van der waals strain and torsional strain is equivalent to the first eclipsed form we saw in Fig 4-c and is 3.8 kcal/mole above in energy state compared to the anti conformer.(See Fig 4-f below)
A sixth 60 degree rotation will bring us back to the anti conformer. At room temperature, there is more than enough kinetic energy in the environment to overcome these energy barriers and allow the rotation about the sigma bond between the C2 and C3 carbons of Butane to be unhindered.
This rotation at room temperature is so rapid that we are not able to detect the individual conformers. It is similar to what happens when one tries to capture a very rapid event on film. If the shutter speed of the camera is much slower than the rapidly occuring event, then the event will be a blur at best, and a distinct picture of it will be impossible. One has to either speed up the shutter speed or slow down the event. With sigma bond rotation, we can slow down the event (rotational speed) by lowering the temperature of the environment to well below 0 Celsius. This slows down molecular motion since the Kinetic energy is reduced. The rotational speed is reduced because there is no longer as much Kinetic Energy to draw upon to get through the energy barriers that must be traversed during the rotation.(See Fig 4 below) There comes a point where there is not enough energy available to overcome these energy barriers, and the molecule settles for the most stable (lowest energy) anti conformer. This would also be true were we to lower the temperature of Ethane in the above section.
Return to the top of the page
Cycloalkanes beginning with the smallest possible member, cyclopropane, will have different stabilities. Generally, we can determine the relative stabilities of these cycloalkanes by experimentally determining their heats of combustion. This is the energy that is released when the cycloalkane is burned in the presence of excess Oxygen inside of a combustion chamber known as a bomb calorimeter. An accurately weighed amount of the organic hydrocarbon is measured out and placed within the chamber of the calorimeter whose Heat Capacity has been determined. The calorimeter is sealed, and pure Oxygen is pumped into the calorimeter. An ignition spark ignites the reaction, and the end products (provided there is excess Oxygen in the chamber) are Carbon Dioxide, Water, and, most importantly, thermal energy. The thermal energy heats up the environment around the calorimeter. Knowing the Heat Capacity of the calorimeter and the heat absorbed by whatever else is in the enviroment (usually the calorimeter is submerged in a container of water with known mass)the temperature change of the environment can be recorded. One can then determine the amount of Heat Energy released for the weighed amount of the organic hydrocarbon used. This release of thermal energy is then converted to a per mole basis, and this is the Heat of Combustion for the organic hydrocarbon.
One problem that hampers a fair comparison of the relative stabilities of cycloalkanes is the fact that different numbers of carbons are involved in the comparison (3, 4, 5, 6, such carbons per molecule) This would bias the results in favor of the larger molecules having the greater number of CH2 groups in the ring. In order to prevent this, we divide the experimentally determined Heat of Combustion by the number of carbons in order to get a Heat of Combustion per Carbon. That would be a much fairer assessment as to the relative stability. Since, in the combustion, the same products are formed regardless of the hydrocarbon, then it is fair to assume that any difference in the Heats of Combustion must be due to the energy state of the original hydrocarbon before combustion takes place. The lower the Heat of Combustion per carbon in the molecule the lower the energy state of the initial hydrocarbon whose stability we are comparing. For example, cyclopropane has a Heat of Combustion per carbon of 166.6 kcal/mol. This is compared to cyclobutane with 164.0 kcal/mol, cyclopentane with 158.7 kcal/mol, and cyclohexane with 157.4 kcal/mol. Notice that cyclopropane has the highest Heat of Combustion, and therefore, should be the highest energy state (less stable) of all four cycloalkanes.
Now the question arises as to why cyclopropane is the least stable followed by cyclobutane (164), cyclopentane (158.7), and cyclohexane (157.4) being the most stable. There are several factors that are influencing these stabilities. The most important is what we call ring strain. Ring strain occurs when the bond angles of the ring carbons are further away from the tetrahedral bond angles preferred by any self respecting sp3 hybridized carbon. The preferred bond angle for sp3 carbons is 109.5 degrees. However, in cyclopropane, the bond angles must be 60 degrees to maintain the ring structure. This means that the carbons are forced to have a bond angle that is 109.5-60 or 49.5 degrees away from the comfortable preferred tetrahedral angle (See Fig 5-a. The greater this difference the greater the strain within the ring system. For cyclobutane where the bond angles necessary to maintain the ring structure is 90 degrees, the ring strain is not quite as much. It is only 109.5-90 or 19.5 degrees away from the preferred tetrahedral angle of the sp3 hybridized carbons within the ring system.(See Fig 5-b below) For cyclopentane the bond angles to maintain the ring structure must be 108 degrees which is only 1.5 degrees from the tetrahedral angle so the ring strain is only 1.5 degrees (See Fig 5-d below). Cyclohexane will have 109.5 degrees bond angles to maintain the ring structure which is exactly what an sp3 carbon prefers. Hence there is no ring strain in cyclohexane which explains its stability in comparison with smaller ring systems (See Fig 5-d below.
Notice that in the four cycloalkanes above as the ring strain increased the ring system was less stable. The concept of ring strain seems to do a good job explaining the Heats of Combustion results in the above situation.
Cycloalkanes of seven carbons or greater seem to be slightly less stable than cyclohexane, but the stability seems to level off after cycloheptane. This leveling off of the stability is due to slight van der waals strain that occurs from atoms across the ring. This steric strain is possible because these ring systems tend to "pucker" like an accordian placing the groups across the ring from one another closer in proximity. This is called "Transanular Interactions".
Return to the top of the page.
As we saw above, cyclohexane seems to be the most stable of the cycloalkanes. Even though cycloalkanes have restricted rotation about the sigma bonds between the ring carbons, there is some limited rotation enough so that cyclohexane does have conformers. Of the several conformers of cyclcohexane, the most stable is the chair conformer. This conformer's stability can be attributed to the minimal van der waals strain of the Hydrogens of the C1 and C4 carbons in the ring. In the chair conformer, these positions are the head rest and the foot rest(See Fig 6-a below). In addition to the minimal steric strain at these positions, there is also minimal torsional strain between adjacent carbons since the hydrogens on these carbons in the ring are staggered. The chair conformer of cyclohexane will undergo a "ring flip" in which the C1 carbon goes from being the head rest to being the foot rest, and the foot rest becomes the head rest. This ring flip requires that the molecule go through six different conformers. In order to accomplish the ring flip, the C4 carbon becomes planar with the C2,C3, C5, and C6 carbons in what is called a half chair conformer. This conformer is the least stable being 10.8 kcal/mol more energetic than the chair conformer.(See Fig 6-b below) As the C4 carbon begins to rise above that plane it must twist out of plane the C2,C3,C5, and C6 carbons in what is called the twist boat. This is 5.5 kcal / mol more than the chair.(See Fig 6-c below) The twist boat converts into the boat conformer where the C1 and C4 carbons form the bow and stern of a boat. The other four carbons are planar. The boat conformer is less stable than the chair by 7.1 kcal/mol because of the increased steric strain of the Hydrogens on the C1 and C4 carbons.(See Fig 6-d below) The boat twists in an effort to bring the C1 carbon down below the plane which forms an equivalent twist boat conformer Which is 5.5 kcal/mol more energetic (less stable) than the chair conformer(See Fig 6-e below). The C1 carbon then becomes planar to the C2,C3,C5,C6 carbons to form a half chair conformer equivalent to the above half chair which is 10.8 kcal/mol more energetic than the chair conformer.(See Fig 6-f below). The C1 carbon then moves down below the plane to assume the flipped chair conformer becoming the foot rest. (See Fig 6-g below).
At room temperature there is more than enough energy available for the ring flip to overcome the energy transitions shown in Fig 6 with over one million such conversions taking place, but because of the more stable state of the chair conformer, it is estimated that 99% of the molecules are in that conformation at any given time.
Return to the top of the page.
Not all of the Hydrogens attached to the ring carbons in Cyclohexane are equivalent. We can prove this by replacing all but one of the 12 Hydrogens with Deuterium leaving one position as regular Hydrogen. Because the ring flip occurs so rapidly at room temperature, there will be only one nuclear magnetic resonance signal for the one Hydrogen. Deuterium atoms do not have a spin state that would generate an NMR signal. However when we slow the molecular motion down by lowering the temperature of the sample to an extremely low temperature so the ring flip occurs much less rapidly, we observe two separate nmr signals with slightly different chemical shifts. This would indicate that the Hydrogen has changed positions as the ring underwent flipping so that the two positions are non-equivalent. These two non-equivalent Hydrogen positions are called the axial and equatorial positions. The axial Hydrogens are those sigma bonds that are parallel to an imaginary axis running through the ring structure (See Fig 7-a). The axial bonds run vertical to the molecule. The equatorial Hydrogens are those whose sigma bonds are perpindicular to that axis (See Fig 7-a below). The equatorial bonds run approximately horizontal to the molecule. During the ring flip process the axial Hydrogens become equatorial and the equatorial Hydrogens become axial. (See Fig 7-b below)
Return to the top of the page.
For mono-substituted cyclohexanes such as Methyl Cyclohexane will have the most stable conformer when the Methyl group is in the equatorial position.(See Fig 8-a below) The steric strain due to the methyl group being very close to the C3 and C5 Hydrogens in the axial position would make the conformer where the Methyl group is in the axial position less stable. (See Fig 8-b below). This steric strain would be much less when the methyl group or any group occupies the equatorial position.
In disubstituted cyclohexanes due to the restricted rotation about the sigma bonds of the ring carbons, cis-trans isomerism is possible. Depending upon which carbons the two groups are located the groups will be attached to the axial or equatorial positions. For the 1,2-di-substituted and 1,4-disubstituted cyclohexanes, the trans isomer will have both groups in the axial(See Fig 9-b below) or in the equatorial positions.(See Fig 9-a below). In that case the more stable conformer would have the two bulky groups in the equatorial positions and in the equilibrium mixture the major conformer would be where both were equatorial.
The cis isomer would have one group on the axial position and the second group in the equatorial position.(See Fig 10-a below) In the flipped conformer, the groups would be equatorial and axial (See Fig 10-b below). Under these conditions, there would always be a bulky group in the axial position regardless of which flipped conformer you considered. In an equilibrium mixture there would be equal amounts of the two conformers since they would be equally stable. (See Fig 10)
For the 1,3 disubstituted cyclohexanes, the trans isomer will have the first group in the axial position and the second group on the equatorial position.(See Fig 11-a below). The flipped conformer will have the first in the equatorial and the second in the axial position (See Fig 11-b below) The trans-1,3 di-substituted cyclohexane conformers are equally stable and so would be equal in amount in an equilibrium mixture.
The cis isomer will have both groups in the axial position (See Fig 12-a below) or in the equatorial position (See Fig 12-b below) (in flipped conformer). In this case the more stable conformer would be where both are in the equatorial position and would constitute the major conformer in an equilibrium mixture.
The stability of the cis-trans isomers of the disubstituted cyclohexanes would depend upon where the bulky groups were. In general, the bulky groups should be as far away from the C3 and C5 Hydrogens as possible. Since these Hydrogens are in the axial position, then the bulky groups would have to be in the equatorial positions if possible.
For example, In the 1,2 dimethylcyclohexanes and in the 1,4-dimethylcyclohexanes the trans isomer would have the two methyl groups either in the axial positions at the same time or in the equatorial positions. Since having them in the equatorial positions would distance them as far away from the C3 and C5 Hydrogens, then this would be considered the most stable conformer.(See Fig 9 above) Low temperature NMR studies show that the equilibrum mixture of the two ring flips would show greater number of Methyl proton signals in the equatorial postion than in the axial according to the chemical shift data.
On the other hand the cis 1,2 isomer would have one methyl in the axial and one in the equatorial postions so the two flipped ring systems that would be in equilibrium would be equal in numbers of molecules in each conformer.(See Fig 10) That is because there will always be one of the bulky Methyl groups in the axial position regardless of which flipped conformer was present. Low temperature NMR studies show that there are equal numbers of Methyl protons in the equilibrium position.
For the 1,3-Dimethylcyclohexane the trans isomer would have the two Methyl groups one in the equatorial and one in the axial position. Again because the each Methyl group is in opposite positions the two flipped conformers are equally stable as in the cis 1,2 and 1,4-Dimethylcyclohexanes above and the equilibrium mixture would have equal numbers of the two conformers(See Fig 11 above). For the cis-1,3-Dimethylcyclohexane, the two Methyl groups will be either in the equatorial or both in the axial positions. The more stable conformer would have them in the equatorial positions as was the case in the Trans-1,2 and Trans-1,4-Dimethylcyclohexanes. Therefore in an equilibrium mixture, there would be far more molecules of the conformer where the two methyl groups were in di-equatorial position(See Fig 12 above)
Return to the top of the page
Or Return to Stereoisomer menu
Return to Organic Page
R. H. Logan, Instructor of Chemistry, Dallas County Community College District, North Lake College.
Send Comments to R.H. Logan:
All textual content copyrighted (c) 1997 R.H. Logan, Instructor of Chemistry, DCCCD All Rights reserved